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3 years ago

Factor completely. 36c2−84cd+49d2=

Mathematics

1 answer:

spayn [35]3 years ago

7 0

Answer:

(6c-7d)^2

Step-by-step explanation:

Factor using the perfect square rule

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Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$

This is the slope of the tangent line, which has equation

$y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}$

7 0

3 years ago

. Compute the required sample size given the required confidence in the sample results is 99.74% (Z score of 3). The level of al

Shtirlitz [24]

Answer:

900 sample size

Step-by-step explanation:

To determine the sample size for a proportion, the margin of error formula is used to determine this:

$E=Z_{\frac{\alpha}{2} }*\sqrt{\frac{\hat p \hat q}{{n} }$

$n=\hat p \hat q*(\frac{Z_{\frac{\alpha}{2} }}{E} )^2$

Where p is the proportion, E is the margin of error, n is the sample size, q = 1 - p, $Z_\frac{\alpha }{2}$ is the z score.

Since the proportion is not known, the sample size needed to guarantee the confidence interval and error is at p = 0.5 and q = 1 - p = 1 - 0.5 = 0.5

E = 5% = 0.05, $Z_\frac{\alpha }{2}$ = 3. Hence:

$n=0.5*0.5*(\frac{3}{0.05} )^2\\\\n = 900$

6 0

3 years ago

A customer buys three packets of cookies that

MArishka [77]

11.43 hope you have a good day

7 0

2 years ago

Read 2 more answers

What is the solution to the equation √8x=√4+2x?

dolphi86 [110]

Answer:

0.3333333333333...........

7 0

4 years ago

NEED HELP ASAP.....At the 2012 Summer Olympic Games in London, in the Men's Shot Put qualifying round, the distances ranged from

jeka57 [31]

Answer:

About 6 athletes.

Step-by-step explanation:

We are concerned only with the percent of athletes that are above one standard deviation.

Between one standard deviation and two standard deviations, there is 13.6% of the athletes.

From 2 to 3, there is 2.1%. Above 3, there is 0.2%.

The sum of those percentages is 15.9% of 40 = 0.159 · 40 = 6.36 or about 6 athletes.

Hope this helps.

6 0

4 years ago